0=25x^2+45x-169

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Solution for 0=25x^2+45x-169 equation:


Simplifying
0 = 25x2 + 45x + -169

Reorder the terms:
0 = -169 + 45x + 25x2

Solving
0 = -169 + 45x + 25x2

Solving for variable 'x'.

Combine like terms: 0 + 169 = 169
169 + -45x + -25x2 = -169 + 45x + 25x2 + 169 + -45x + -25x2

Reorder the terms:
169 + -45x + -25x2 = -169 + 169 + 45x + -45x + 25x2 + -25x2

Combine like terms: -169 + 169 = 0
169 + -45x + -25x2 = 0 + 45x + -45x + 25x2 + -25x2
169 + -45x + -25x2 = 45x + -45x + 25x2 + -25x2

Combine like terms: 45x + -45x = 0
169 + -45x + -25x2 = 0 + 25x2 + -25x2
169 + -45x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
169 + -45x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-6.76 + 1.8x + x2 = 0

Move the constant term to the right:

Add '6.76' to each side of the equation.
-6.76 + 1.8x + 6.76 + x2 = 0 + 6.76

Reorder the terms:
-6.76 + 6.76 + 1.8x + x2 = 0 + 6.76

Combine like terms: -6.76 + 6.76 = 0.00
0.00 + 1.8x + x2 = 0 + 6.76
1.8x + x2 = 0 + 6.76

Combine like terms: 0 + 6.76 = 6.76
1.8x + x2 = 6.76

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 6.76 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 6.76 + 0.81

Combine like terms: 6.76 + 0.81 = 7.57
0.81 + 1.8x + x2 = 7.57

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 7.57

Calculate the square root of the right side: 2.751363298

Break this problem into two subproblems by setting 
(x + 0.9) equal to 2.751363298 and -2.751363298.

Subproblem 1

x + 0.9 = 2.751363298 Simplifying x + 0.9 = 2.751363298 Reorder the terms: 0.9 + x = 2.751363298 Solving 0.9 + x = 2.751363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.751363298 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.751363298 + -0.9 x = 2.751363298 + -0.9 Combine like terms: 2.751363298 + -0.9 = 1.851363298 x = 1.851363298 Simplifying x = 1.851363298

Subproblem 2

x + 0.9 = -2.751363298 Simplifying x + 0.9 = -2.751363298 Reorder the terms: 0.9 + x = -2.751363298 Solving 0.9 + x = -2.751363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.751363298 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.751363298 + -0.9 x = -2.751363298 + -0.9 Combine like terms: -2.751363298 + -0.9 = -3.651363298 x = -3.651363298 Simplifying x = -3.651363298

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.851363298, -3.651363298}

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